Let’s go through the step-by-step solution to compute the sine and cosine of ( 330^\\circ ) using the reference angle.<\/p>\n\n\n\n
Step 1: Find the Reference Angle<\/strong><\/h3>\n\n\n\nThe reference angle is the acute angle between the given angle and the x-axis. It is found by subtracting the given angle from ( 360^\\circ ) if the angle is in Quadrant IV.<\/p>\n\n\n\n
[
\\text{Reference Angle} = 360^\\circ – 330^\\circ = 30^\\circ
]<\/p>\n\n\n\n
Answer for part (a):<\/strong> The reference angle is 30\u00b0<\/strong>.<\/p>\n\n\n\n
\n\n\n\nStep 2: Determine the Quadrant<\/strong><\/h3>\n\n\n\nThe given angle is ( 330^\\circ ). To determine the quadrant, we check where it falls:<\/p>\n\n\n\n
\n- Quadrant I: ( 0^\\circ ) to ( 90^\\circ )<\/li>\n\n\n\n
- Quadrant II: ( 90^\\circ ) to ( 180^\\circ )<\/li>\n\n\n\n
- Quadrant III: ( 180^\\circ ) to ( 270^\\circ )<\/li>\n\n\n\n
- Quadrant IV: ( 270^\\circ ) to ( 360^\\circ )<\/li>\n<\/ul>\n\n\n\n
Since ( 330^\\circ ) is between ( 270^\\circ ) and ( 360^\\circ ), it is in Quadrant IV<\/strong>.<\/p>\n\n\n\nAnswer for part (b):<\/strong> The angle is in Quadrant 4<\/strong>.<\/p>\n\n\n\n
\n\n\n\nStep 3: Find the Sine and Cosine Values<\/strong><\/h3>\n\n\n\nSince the reference angle is ( 30^\\circ ), we use the known trigonometric values:<\/p>\n\n\n\n
[
\\sin 30^\\circ = \\frac{1}{2}, \\quad \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
\n- In Quadrant IV, sine is negative<\/strong> and cosine is positive<\/strong>.<\/li>\n\n\n\n
- Therefore:<\/li>\n<\/ul>\n\n\n\n
[
\\sin 330^\\circ = -\\sin 30^\\circ = -\\frac{1}{2}
]<\/p>\n\n\n\n
[
\\cos 330^\\circ = \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers<\/strong><\/h3>\n\n\n\n(c)<\/strong> ( \\sin(330^\\circ) = -\\frac{1}{2} )
(d)<\/strong> ( \\cos(330^\\circ) = \\frac{\\sqrt{3}}{2} )<\/p>\n\n\n\n
\n\n\n\nExplanation<\/strong><\/h3>\n\n\n\nThe reference angle helps us find trigonometric values by reducing the given angle to an equivalent acute angle between ( 0^\\circ ) and ( 90^\\circ ). Since ( 330^\\circ ) is in Quadrant IV, sine is negative and cosine is positive. By using the known values of sine and cosine for ( 30^\\circ ), we can determine the exact values for ( 330^\\circ ).<\/p>\n\n\n\n
Now, let me generate an image illustrating this concept.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-232-1024x913.png\")
<\/figure>\n\n\n\nHere is an illustration of the unit circle showing the angle ( 330^\\circ ), its reference angle ( 30^\\circ ), and the corresponding cosine and sine values. This visual helps to understand why (\\sin 330^\\circ = -\\frac{1}{2}) and (\\cos 330^\\circ = \\frac{\\sqrt{3}}{2}). <\/p>\n","protected":false},"excerpt":{"rendered":"
Compute the sine and cosine of 330\u2218 by using the reference angle. a.) What is the reference angle? degrees. b.)In what quadrant is this angle? (answer 1, 2, 3, or 4) c.) sin(330\u2218)= d.) cos(330\u2218)= The correct answer and explanation is : Let’s go through the step-by-step solution to compute the sine and cosine of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-196581","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=196581"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{Reference Angle} = 360^\\circ – 330^\\circ = 30^\\circ
]<\/p>\n\n\n\n
\n\n\n\n
Step 2: Determine the Quadrant<\/strong><\/h3>\n\n\n\nThe given angle is ( 330^\\circ ). To determine the quadrant, we check where it falls:<\/p>\n\n\n\n
\n- Quadrant I: ( 0^\\circ ) to ( 90^\\circ )<\/li>\n\n\n\n
- Quadrant II: ( 90^\\circ ) to ( 180^\\circ )<\/li>\n\n\n\n
- Quadrant III: ( 180^\\circ ) to ( 270^\\circ )<\/li>\n\n\n\n
- Quadrant IV: ( 270^\\circ ) to ( 360^\\circ )<\/li>\n<\/ul>\n\n\n\n
Since ( 330^\\circ ) is between ( 270^\\circ ) and ( 360^\\circ ), it is in Quadrant IV<\/strong>.<\/p>\n\n\n\nAnswer for part (b):<\/strong> The angle is in Quadrant 4<\/strong>.<\/p>\n\n\n\n
\n\n\n\nStep 3: Find the Sine and Cosine Values<\/strong><\/h3>\n\n\n\nSince the reference angle is ( 30^\\circ ), we use the known trigonometric values:<\/p>\n\n\n\n
[
\\sin 30^\\circ = \\frac{1}{2}, \\quad \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
\n- In Quadrant IV, sine is negative<\/strong> and cosine is positive<\/strong>.<\/li>\n\n\n\n
- Therefore:<\/li>\n<\/ul>\n\n\n\n
[
\\sin 330^\\circ = -\\sin 30^\\circ = -\\frac{1}{2}
]<\/p>\n\n\n\n
[
\\cos 330^\\circ = \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers<\/strong><\/h3>\n\n\n\n(c)<\/strong> ( \\sin(330^\\circ) = -\\frac{1}{2} )
(d)<\/strong> ( \\cos(330^\\circ) = \\frac{\\sqrt{3}}{2} )<\/p>\n\n\n\n
\n\n\n\nExplanation<\/strong><\/h3>\n\n\n\nThe reference angle helps us find trigonometric values by reducing the given angle to an equivalent acute angle between ( 0^\\circ ) and ( 90^\\circ ). Since ( 330^\\circ ) is in Quadrant IV, sine is negative and cosine is positive. By using the known values of sine and cosine for ( 30^\\circ ), we can determine the exact values for ( 330^\\circ ).<\/p>\n\n\n\n
Now, let me generate an image illustrating this concept.<\/p>\n\n\n\n<\/figure>\n\n\n\nHere is an illustration of the unit circle showing the angle ( 330^\\circ ), its reference angle ( 30^\\circ ), and the corresponding cosine and sine values. This visual helps to understand why (\\sin 330^\\circ = -\\frac{1}{2}) and (\\cos 330^\\circ = \\frac{\\sqrt{3}}{2}). <\/p>\n","protected":false},"excerpt":{"rendered":"
Compute the sine and cosine of 330\u2218 by using the reference angle. a.) What is the reference angle? degrees. b.)In what quadrant is this angle? (answer 1, 2, 3, or 4) c.) sin(330\u2218)= d.) cos(330\u2218)= The correct answer and explanation is : Let’s go through the step-by-step solution to compute the sine and cosine of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-196581","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=196581"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Since ( 330^\\circ ) is between ( 270^\\circ ) and ( 360^\\circ ), it is in Quadrant IV<\/strong>.<\/p>\n\n\n\n Answer for part (b):<\/strong> The angle is in Quadrant 4<\/strong>.<\/p>\n\n\n\n Since the reference angle is ( 30^\\circ ), we use the known trigonometric values:<\/p>\n\n\n\n [ [ [ (c)<\/strong> ( \\sin(330^\\circ) = -\\frac{1}{2} ) The reference angle helps us find trigonometric values by reducing the given angle to an equivalent acute angle between ( 0^\\circ ) and ( 90^\\circ ). Since ( 330^\\circ ) is in Quadrant IV, sine is negative and cosine is positive. By using the known values of sine and cosine for ( 30^\\circ ), we can determine the exact values for ( 330^\\circ ).<\/p>\n\n\n\n Now, let me generate an image illustrating this concept.<\/p>\n\n\n\n Here is an illustration of the unit circle showing the angle ( 330^\\circ ), its reference angle ( 30^\\circ ), and the corresponding cosine and sine values. This visual helps to understand why (\\sin 330^\\circ = -\\frac{1}{2}) and (\\cos 330^\\circ = \\frac{\\sqrt{3}}{2}). <\/p>\n","protected":false},"excerpt":{"rendered":" Compute the sine and cosine of 330\u2218 by using the reference angle. a.) What is the reference angle? degrees. b.)In what quadrant is this angle? (answer 1, 2, 3, or 4) c.) sin(330\u2218)= d.) cos(330\u2218)= The correct answer and explanation is : Let’s go through the step-by-step solution to compute the sine and cosine of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-196581","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=196581"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196581\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 3: Find the Sine and Cosine Values<\/strong><\/h3>\n\n\n\n
\\sin 30^\\circ = \\frac{1}{2}, \\quad \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n\n
\\sin 330^\\circ = -\\sin 30^\\circ = -\\frac{1}{2}
]<\/p>\n\n\n\n
\\cos 330^\\circ = \\cos 30^\\circ = \\frac{\\sqrt{3}}{2}
]<\/p>\n\n\n\n
\n\n\n\nFinal Answers<\/strong><\/h3>\n\n\n\n
(d)<\/strong> ( \\cos(330^\\circ) = \\frac{\\sqrt{3}}{2} )<\/p>\n\n\n\n
\n\n\n\nExplanation<\/strong><\/h3>\n\n\n\n
<\/figure>\n\n\n\n